Maybe try to replace the font with something that fits your needs? winetricks should be your friend to install new fonts into that prefix. Maybe the dpi of wine is high? Check it with winecfg. It has nothing to do with gnome3.
I have used this one to install the game. The font on the screenshot is one of “best” looking fonts - the other are … let’s just say NOK. I went at some point to add allfont package
I have played a bit with the Winetricks and tested font smooting bgr, disable, gray and rgb options. In my case the rgb option look better overall.
I have followed your your advice to change the DPI I went from 96 to 480+ (now I have to look fo a way to decrease it, as the slider is out of screen), yet no joy.
Edit: found it 5 times tab + 11 left arrow brings it back to 96 DPI.
This is irregular for certain. I assume you installed the game via the supplied lutris script?
What wine version are you using? Lutris 5.7.8 works best I have found, my fonts and the battle.net window decorations are perfect.